Recherche:Techniques de régressions au plus près/Fonctions régressives Fi communes de base

**Fonctions régressives Fi communes de base**
Recherche : Techniques de régressions au plus près

Chapitre n^o 3
Chap. préc. :	Définition de la régression au plus près
Chap. suiv. :	Fonctions régressives Fi communes composées

En raison de limitations techniques, la typographie souhaitable du titre, « Techniques de régressions au plus près : Fonctions régressives Fi communes de base
Techniques de régressions au plus près/Fonctions régressives Fi communes de base », n'a pu être restituée correctement ci-dessus.

Fonctions régressives Fi communes de base modifier

Dans les approches B et C modifier

Fonctions paires pour partie paire modifier

Fonctions régressives de base paires modifier

Type F(x) Degré	Monôme	Cosinus trigonométrique	Tangente trigonométrique	Cosinus hyperbolique	Tangente hyperbolique	Exponentielle	Construite avec $f(x)$
0 1 -1	$1$	$1-\cos(\omega x)$ $1-\cos ^{-1}(\omega x)$ $1-\cos(\omega x^{-1})$ $1-\cos ^{-1}(\omega x^{-1})$ $1-\cos(\omega x^{2})$ $1-\cos ^{-1}(\omega x^{2})$	$\tan(\omega x^{2})$ $\tan ^{-1}(\omega x^{2})$ $\tan(\omega x^{-2})$ $\tan ^{-1}(\omega x^{-2})$	$1-\cosh(\omega x)$ $1-\cosh ^{-1}(\omega x)$ $1-\cosh(\omega x^{-1}$ $1-\cosh ^{-1}(\omega x{-1})$ $1-\cos(\omega x^{2})$ $1-\cos ^{-1}(\omega x^{2})$	$\tanh(\omega x^{2})$ $\tanh ^{-1}(\omega x^{2})$ $\tanh(\omega x^{-2})$ $\tanh ^{-1}(\omega x^{-2})$	$1-\exp(\omega x^{2})$ $1-\exp ^{-1}(\omega x^{2})$ $1-\exp(\omega x^{2})$ $1-\exp ^{-1}(\omega x^{2})$	$F(x)=f(0)-f(x)$ si x>0 ET $F(x)=f(0)-f(-x)$ si x<0
2	$x^{2}$ $x^{-2}$	$1-\cos ^{2}(\omega x)$ $1-\cos ^{-2}(\omega x)$ $1-\cos ^{2}(\omega x^{-1})$ $1-\cos ^{-2}(\omega x^{-1})$	$\tan ^{2}(\omega x)$ $\tan ^{-2}(\omega wx)$ $\tan ^{2}(\omega x^{-1})$ $\tan ^{-2}(\omega x^{-1})$	$1-\cosh ^{2}(\omega x)$ $1-\cosh ^{-2}(\omega x)$ $1-\cosh ^{2}(\omega x^{-1})$ $1-\cosh ^{-2}(\omega x^{-1})$	$\tanh ^{2}(\omega x)$ $\tanh ^{-2}(\omega wx)$ $\tanh ^{2}(\omega x^{-1})$ $\tanh ^{-2}(\omega x^{-1})$	$1-\exp ^{2}(\omega x)$ $1-\exp ^{-2}(\omega x)$ $1-\exp ^{2}(\omega x^{-1})$ $1-\exp ^{-2}(\omega x^{-1})$	$F(x)=f(0)-f^{2}(x)$ si x>0 ET $F(x)=f^{2}(0)-f^{2}(-x)$ si x<0
n m	$x^{2n}$ $x^{-2n}$	$1-\cos ^{n}(\omega x)$ $1-\cos(\omega x^{m})$ $1-\cos ^{n}(\omega x^{m})$	$\tan ^{2n}(\omega x)$ $\tan ^{-2n}(\omega x)$ $\tan ^{2n}(\omega x^{m})$	$1-\cosh ^{n}(\omega x)$ $1-\cosh(\omega x^{m})$ $1-\cosh ^{n}(\omega x^{m})$	$\tanh ^{2n}(\omega x)$ $\tanh ^{-2n}(\omega x)$ $\tanh ^{2n}(\omega x^{m})$	$1-\exp ^{n}(\omega x^{2m})$ $1-\exp ^{n}(-\omega x^{2m})$	$F(x)=f(0)-f^{n}(x^{2m})$ si x>0 ET $F(x)=f^{n}(0)-f^{n}(-x^{2m})$ si x<0
général	$m\in {\mathbb {Z} },n\in {\mathbb {R} }$	$m\in {\mathbb {Z} },n\in {\mathbb {R} }$	$m\in {\mathbb {Z} },n\in {\mathbb {R} }$	$m\in {\mathbb {Z} },n\in {\mathbb {R} }$	$m\in {\mathbb {Z} },n\in {\mathbb {R} }$	$m\in {\mathbb {Z} },n\in {\mathbb {R} }$	$m\in {\mathbb {Z} },n\in {\mathbb {R} }$

Fonctions régressives composées paires modifier

À FINIR 3 premières cellules faites

Type
MonômeAVEC Sin Cos Sinh Cosh Tan Tanh Exp	$x^{2l/2l+1}\times \sin ^{2m/2m+1}(\omega x)$ XXXXXXXXXXXXXXXXXXXXXXXX $x^{2l/2l+1}\times \sinh ^{2m/2m+1}(\omega x)$ XXXXXXXXXXXXXXXXXXXXXXXX $x^{2l/2l+1}\times \tan ^{2m/2m+1}(\omega x)$ $x^{2l/2l+1}\times \tanh ^{2m/2m+1}(\omega x)$ XXXXXXXXXXXXXXXXXXXXXXXX	$x^{2l}\times \sin ^{m}(\omega x^{2})$ $x^{2l}\times \cos ^{m}(\omega x^{2})$ $x^{2l}\times \sinh ^{m}(\omega x^{2})$ $x^{2l}\times \cosh ^{m}(\omega x^{2})$ $x^{2l}\times \tan ^{m}(\omega x^{2})$ $x^{2l}\times \tanh ^{m}(\omega x^{2})$ $x^{2l}\times \exp ^{m}(\omega x^{2})$	$x^{2l}\times \sin ^{2m}(\omega x)$ $x^{2l}\times \cos ^{m}(\omega x)$ $x^{2l}\times \sinh ^{2m}(\omega x)$ $x^{2l}\times \cos ^{m}(\omega x)$ $x^{2l}\times \tan ^{2m}(\omega x)$ $x^{2l}\times \tanh ^{2m}(\omega x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX	$x^{2l+1}\times \sin ^{2m}(\omega x^{2n+1})$ / $x^{2l+1}\times \sin ^{m}(\omega x^{2n})$ / $x^{2l}\times \sin ^{2m+1}(\omega x^{2n+1})$ $x^{2l+1}\times \cos ^{2m}(\omega x^{2n+1})$ / $x^{2l+1}\times \cos ^{m}(\omega x^{2n})$ /XXXXXXXXXXXXXXXXXXXXXXXXXXXX $x^{2l+1}\times \sinh ^{2m}(\omega x^{2n+1})$ / $x^{2l+1}\times \sinh ^{m}(\omega x^{2n})$ / $x^{2l}\times \sinh ^{2m+1}(\omega x^{2n+1})$ $x^{2l+1}\times \cosh ^{2m}(\omega x^{2n+1})$ / $x^{2l+1}\times \cosh ^{m}(\omega x^{2n})$ /XXXXXXXXXXXXXXXXXXXXXXXXXXXX $x^{2l+1}\times \tan ^{2m+1}(\omega x^{2n+1})$ / $x^{2l+1}\times \tan ^{m}(\omega x^{2n})$ / $x^{2l}\times \tan ^{2m+1}(\omega x^{2n+1})$ $x^{2l+1}\times \tanh ^{2m}(\omega x^{2n+1})$ / $x^{2l+1}\times \tanh ^{m}(\omega x^{2n})/x^{2l}\times \tanh ^{2m+1}(\omega x^{2n+1})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXX / $x^{2l+1}\times \exp ^{m}(\omega x^{2n})$ / XXXXXXXXXXXXXXXXXXXXXXXXXXXX
SinusAVEC Sin Cos Sinh Cosh Tan Tanh Exp	$\sin(\omega _{1}x)\times \sin ^{2m}(\omega _{2}x)$ $\sin(\omega _{1}x)\times \cos ^{m}(\omega _{2}x)$ $\sin(\omega _{1}x)\times \sinh ^{2m}(\omega _{2}x)$ $\sin(\omega _{1}x)\times \cosh ^{m}(\omega _{2}x)$ $\sin(\omega _{1}x)\times \tan ^{2m}(\omega _{2}x)$ $\sin(\omega _{1}x)\times \tanh ^{2m}(\omega _{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXX	$\sin(\omega _{1}x^{2l+1})\times \sin ^{m}(\omega x^{2})$ $\sin(\omega _{1}x^{2l+1})\times \cos ^{m}(\omega x^{2})$ $\sin(\omega _{1}x^{2l+1})\times \sinh ^{m}(\omega x^{2})$ $\sin(\omega _{1}x^{2l+1})\times \cosh ^{m}(\omega x^{2})$ $\sin(\omega _{1}x^{2l+1})\times \tan ^{m}(\omega x^{2})$ $\sin(\omega _{1}x^{2l+1})\times \tanh ^{m}(\omega x^{2})$ $\sin(\omega _{1}x^{2l+1})\times \exp ^{m}(\omega x^{2})$	$\sin(\omega _{1}x^{2l})\times \sin ^{2m+1}(\omega _{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX $\sin(\omega _{1}x^{2l})\times \sinh ^{2m+1}(\omega _{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX $\sin(\omega _{1}x^{2l})\times \tan ^{2m+1}(\omega _{2}x)$ $\sin(\omega _{1}x^{2l})\times \tanh ^{2m+1}(\omega _{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX	$\sin(\omega _{1}x^{2l+1})\times \sin ^{2m}(\omega _{2}x^{2n+1})$ / $\sin(\omega _{1}x^{2l+1})\times \sin ^{m}(\omega _{2}x^{2n})$ / $\sin(\omega _{1}x^{2l})\times \sin ^{2m+1}(\omega _{2}x^{2n+1})$ $\sin(\omega _{1}x^{2l+1})\times \cos ^{2m}(\omega _{2}x^{2n+1})$ / $\omega _{1}sin(x^{2l+1})\times \cos ^{m}(\omega _{2}x^{2n})$ /XXXXXXXXXXXXXXXXXXXXXXXXXXXX $\sin(\omega _{1}x^{2l+1})\times \sinh ^{2m}(\omega _{2}x^{2n+1})$ / $\sin(\omega _{1}x^{2l+1})\times \sinh ^{m}(\omega _{2}x^{2n})$ / $\sin(\omega _{1}x^{2l})\times \sinh ^{2m+1}(\omega _{2}x^{2n+1})$ $\sin(\omega _{1}x^{2l+1})\times \cosh ^{2m}(\omega _{2}x^{2n+1})$ / $\sin(\omega _{1}x^{2l+1})\times \cosh ^{m}(\omega _{2}x^{2n})$ / XXXXXXXXXXXXXXXXXXX $\sin(\omega _{1}x^{2l+1})\times \tan ^{2m}(\omega _{2}x^{2n+1})$ / $\sin(\omega _{1}x^{2l+1})\times \tan ^{m}(\omega _{2}x^{2n})$ / $\sin(\omega _{1}x^{2l})\times \tan ^{2m+1}(\omega _{2}x^{2n+1})$ $\sin(\omega _{1}x^{2l+1})\times \tanh ^{2m}(\omega _{2}x^{2n+1})$ / $\sin(\omega _{1}x^{2l+1})\times \tanh ^{m}(\omega _{2}x^{2n})/\sin(\omega _{1}x^{2l})\times \tanh ^{2m+1}(\omega _{2}x^{2n+1})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXX/ $\sin(\omega _{1}x^{2l+1})\times \exp ^{m}(\omega _{2}x^{2n})$ /XXXXXXXXXXXXXXXXXXXXXXXXXXXX
Cos AVEC Cos Sinh Cosh Tan Tanh Exp	XXXXXXXXXXXXXXXXXXXXXXXX $\cos(\omega _{1}x)\times \sinh ^{2m+1}(\omega _{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXX $\cos(\omega _{1}x)\times \tan ^{2m+1}(\omega _{2}x)$ $\cos(\omega _{1}x)\times \tanh ^{2m+1}(\omega _{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXX	XXXXXXXXXXXXXXXXXXXXXXXXXXXX $\cos(\omega _{1}x^{l})\times \sinh ^{2m+1}(\omega x^{2})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXX $\cos(\omega _{1}x^{l})\times \tan ^{2m+1}(\omega x^{2})$ $\cos(\omega _{1}x^{l})\times \tanh ^{2m+1}(\omega x^{2})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXX	XXXXXXXXXXXXXXXXXXXXXXXXXXX $\cos(\omega _{1}x^{l})\times \sinh ^{2m+1}(\omega _{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX $\cos(\omega _{1}x^{l})\times \tan ^{2m+1}(\omega _{2}x)$ $\cos(\omega _{1}x^{l})\times \tanh ^{2m+1}(\omega _{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX	XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX $\cos(\omega _{1}x^{2l+1})\times \sinh ^{2m+1}(\omega _{2}x^{2n+1})$ / $\cos(\omega _{1}x^{2l+1})\times \sinh ^{2m+1}(\omega _{2}x^{2n})$ / $\cos(\omega _{1}x^{2l})\times \sinh ^{2m+1}(\omega _{2}x^{2n+1})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX $\cos(\omega _{1}x^{2l+1})\times \tan ^{2m+1}(\omega _{2}x^{2n+1})$ / $\cos(\omega _{1}x^{2l+1})\times \tan ^{2m+1}(\omega _{2}x^{2n})$ / $\cos(\omega _{1}x^{2l})\times \tan ^{2m+1}(\omega _{2}x^{2n+1})$ $\cos(\omega _{1}x^{2l+1})\times \tanh ^{2m+1}(\omega _{2}x^{2n+1})$ / $\cos(\omega _{1}x^{2l+1})\times \tanh ^{2m+1}(\omega _{2}x^{2n})/\cos(\omega _{1}x^{2l})\times \tanh ^{2m+1}(\omega _{2}x^{2n+1})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
Cosh AVEC Sinh Cosh Tan Tanh Exp	$\cosh(\omega _{1}x)\times \sinh ^{2m+1}(\omega _{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXX $\cosh(\omega _{1}x)\times \tan ^{2m+1}(\omega _{2}x)$ $\cosh(\omega _{1}x)\times \tanh ^{2m+1}(\omega _{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXX	$\cosh(\omega _{1}x^{l})\times \sinh ^{2m+1}(\omega x^{2})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXX $\cosh(\omega _{1}x^{l})\times \tan ^{2m+1}(\omega x^{2})$ $\cosh(\omega _{1}x^{l})\times \tanh ^{2m+1}(\omega x^{2})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXX	$\cosh(\omega _{1}x^{l})\times \sinh ^{2m+1}(\omega _{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX $\cosh(\omega _{1}x^{l})\times \tan ^{2m+1}(\omega _{2}x)$ $\cosh(\omega _{1}x^{l})\times \tanh ^{2m+1}(\omega _{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX	$\cosh(\omega _{1}x^{2l+1})\times \sinh ^{2m+1}(\omega _{2}x^{2n+1})$ / $\cosh(\omega _{1}x^{2l+1})\times \sinh ^{2m+1}(\omega _{2}x^{2n})$ / $\cosh(\omega _{1}x^{2l})\times \sinh ^{2m+1}(\omega _{2}x^{2n+1})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX $\cosh(\omega _{1}x^{2l+1})\times \tan ^{2m+1}(\omega _{2}x^{2n+1})$ / $\cosh(\omega _{1}x^{2l+1})\times \tan ^{2m+1}(\omega _{2}x^{2n})$ / $\cosh(\omega _{1}x^{2l})\times \tan ^{2m+1}(\omega _{2}x^{2n+1})$ $\cosh(\omega _{1}x^{2l+1})\times \tanh ^{2m+1}(\omega _{2}x^{2n+1})$ / $\cosh(\omega _{1}x^{2l+1})\times \tanh ^{2m+1}(\omega _{2}x^{2n})/\cosh(\omega _{1}x^{2l})\times \tanh ^{2m+1}(\omega _{2}x^{2n+1})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
Tan AVEC Tan Tanh Exp	$\tan(\omega _{1}x)\times \tan ^{2m}(\omega _{2}x)$ $\tan(\omega _{1}x)\times \tanh ^{2m}(\omega _{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXX	$\tan(\omega _{1}x^{2l+1})\times \tan ^{2m+1}(\omega x^{2})$ $\tan(\omega _{1}x^{2l+1})\times \tanh ^{2m+1}(\omega x^{2})$ $\tan(\omega _{1}x^{2l+1})\times \exp ^{m}(\omega x^{2})$	$\tan(\omega _{1}x^{2l})\times \tan ^{2m+1}(\omega _{2}x)$ $\tan(\omega _{1}x^{2l})\times \tanh ^{2m+1}(\omega _{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX	$\tan(\omega _{1}x^{2l+1})\times \tan ^{2m+1}(\omega _{2}x^{2n+1})$ / $\tan(\omega _{1}x^{2l+1})\times \tan ^{2m+1}(\omega _{2}x^{2n})$ / $\tan(\omega _{1}x^{2l})\times \tan ^{2m+1}(\omega _{2}x^{2n+1})$ $\tan(\omega _{1}x^{2l+1})\times \tanh ^{2m}(\omega _{2}x^{2n+1})$ / $\tan(\omega _{1}x^{2l+1})\times \tanh ^{2m+1}(\omega _{2}x^{2n})/\tan(\omega _{1}x^{2l})\times \tanh ^{2m+1}(\omega _{2}x^{2n+1})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
Tanh AVEC Tanh Exp	$\tanh(\omega _{1}x)\times \tanh ^{2m}(\omega _{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXX	$\tanh(\omega _{1}x^{2l+1})\times \tanh ^{2m+1}(\omega x^{2})$ $\tanh(\omega _{1}x^{2l+1})\times \exp ^{m}(\omega x^{2})$	$\tanh(\omega _{1}x^{2l})\times \tanh ^{2m+1}(\omega _{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX	$\tanh(\omega _{1}x^{2l+1})\times \tanh ^{2m}(\omega _{2}x^{2n+1})$ / $\tanh(\omega _{1}x^{2l+1})\times \tanh ^{2m+1}(\omega _{2}x^{2n})/\tanh(\omega _{1}x^{2l})\times \tanh ^{2m+1}(\omega _{2}x^{2n+1})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX $\tan(\omega _{1}x^{2l+1})\times \exp ^{m}(\omega x^{2})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
Construite Approchée

Fonctions composées par 2 paires modifier

AJOUTER TABLEAU DES COMBINéS

Fonctions impaires pour partie impaire modifier

Fonctions de base modifier

Type F(x) Degré	Monôme	Sinus trigonométrique	Tangente trigonométrique	Sinus hyperbolique	Tangente hyperbolique	Exponentielle	Construite avec $f(x)$
0 1 -1	$x$ $x^{-1}$	$\sin(\omega x)$ $\sin ^{-1}(\omega x)$ $\sin(\omega x^{-1})$ $\sin ^{-1}(\omega x^{-1})$	$\tan(\omega x)$ $\tan ^{-1}(\omega x)$ $\tan(\omega x{-1})$ $\tan ^{-1}(\omega x{-1})$	$\sinh(\omega x)$ $\sinh ^{-1}(\omega x)$ $\sinh(\omega x^{-1})$ $\sinh ^{-1}(\omega x^{-1})$	$\tanh(\omega x)$ $\tanh ^{-1}(\omega x)$ $\tanh(\omega x{-1})$ $\tanh ^{-1}(\omega x{-1})$	$-e^{\omega \|x\|}$ si x<0 ET $e^{\omega \|x\|}$ si x>0</math>	$F(x)=f(x)$ si x>0 ET $F(x)=-f(-x)$ si x<0
3	$x^{3}$ $x^{-3}$	$\sin ^{3}(\omega x)$ $\sin ^{-3}(\omega x)$ $\sin ^{3}(\omega x^{-1})$ $\sin ^{-3}(\omega x{-1})$	$\tan ^{3}(\omega x)$ $\tan ^{-3}(\omega x)$ $\tan ^{3}(\omega x{-1})$ $\tan ^{-3}(\omega x{-1})$	$\sinh ^{3}(\omega x)$ $\sinh ^{-3}(\omega x)$ $\sinh ^{3}(\omega x{-1})$ $\sinh ^{-3}(\omega x{-1})$	$\tanh ^{3}(\omega x)$ $\tanh ^{-3}(\omega x)$ $\tanh ^{3}(\omega x{-1})$ $\tanh ^{-3}(\omega x{-1})$	$(-e^{\omega \|x^{3}\|}$ si x>0 ET $e^{\omega \|x^{3}\|}$ si x<0	$F(x)=f^{2}(x)$ si x>0 ET $F(x)=-f^{2}(-x)$ si x<0
2m+1 2n+1	$x^{2n+1}$ $x^{-(2n+1)}$	$\sin ^{2n+1}(\omega x^{2m+1})$ $\sin ^{-(2n+1)}(\omega x^{2m+1})$	$\tan ^{2n+1}(\omega x^{2m+1})$ $\tan ^{-(2n+1)}(\omega x^{2m+1})$	$\sinh ^{2n+1}(\omega x^{2m+1})$ $\sinh ^{-(2n+1)}(\omega x^{2m+1})$	$\tanh ^{2n+1}(\omega x^{2m+1})$ $\tanh ^{-(2n+1)}(\omega x^{2m+1})$	$-e^{\omega \|x^{2m+1}\|}$ si x>0 ET $e^{\omega \|x^{2m+1}\|}$ si x<0	$F(x)=f^{n}(x^{2m+1})$ si x>0 ET $F(x)=-f^{n}(-x^{2m+1})$ si x<0
général	$m\in {\mathbb {Z} },n\in {\mathbb {R} }$	$m\in {\mathbb {Z} },n\in {\mathbb {R} }$	$m\in {\mathbb {Z} },n\in {\mathbb {R} }$	$m\in {\mathbb {Z} },n\in {\mathbb {R} }$	$m\in {\mathbb {Z} },n\in {\mathbb {R} }$	$m\in {\mathbb {Z} },n\in {\mathbb {R} }$	$n\in {\mathbb {R} }$

Fonctions régressives composées impaires modifier

Règles :

Tableau des parités d'un produit à à faire

Type	Degré i/p/i	Degré i/i_p/p	Degré p/i/i	Degré ipi/i-p/pii
MonômeAVEC Sin Cos Sinh Cosh Tan Tanh Exp	$x^{2l+1}\times \sin ^{2m}(\omega x)$ $x^{2l+1}\times \cos ^{2m}(\omega x)$ $x^{2l+1}\times \sinh ^{2m}(\omega x)$ $x^{2l+1}\times \cosh ^{2m}(\omega x)$ $x^{2l+1}\times \tan ^{2m}(\omega x)$ $x^{2l+1}\times \tanh ^{2m}(\omega x)$ XXXXXXXXXXXXXXXXXXXXXXXX	$x^{2l+1}\times \sin ^{m}(\omega x^{2})$ $x^{2l+1}\times \cos ^{m}(\omega x^{2})$ $x^{2l+1}\times \sinh ^{m}(\omega x^{2})$ $x^{2l+1}\times \cosh ^{m}(\omega x^{2})$ $x^{2l+1}\times \tan ^{m}(\omega x^{2})$ $x^{2l+1}\times \tanh ^{m}(\omega x^{2})$ $x^{2l+1}\times \exp ^{m}(\omega x^{2})$	$x^{2l}\times \sin ^{2m+1}(\omega x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX $x^{2l}\times \sinh ^{2m+1}(\omega x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX $x^{2l}\times \tan ^{2m+1}(\omega x)$ $x^{2l}\times \tanh ^{2m+1}(\omega x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX	$x^{2l+1}\times \sin ^{2m}(\omega x^{2n+1})$ / $x^{2l+1}\times \sin ^{m}(\omega x^{2n})$ / $x^{2l}\times \sin ^{2m+1}(\omega x^{2n+1})$ $x^{2l+1}\times \cos ^{2m}(\omega x^{2n+1})$ / $x^{2l+1}\times \cos ^{m}(\omega x^{2n})$ /XXXXXXXXXXXXXXXXXXXXXXXXXXXX $x^{2l+1}\times \sinh ^{2m}(\omega x^{2n+1})$ / $x^{2l+1}\times \sinh ^{m}(\omega x^{2n})$ / $x^{2l}\times \sinh ^{2m+1}(\omega x^{2n+1})$ $x^{2l+1}\times \cosh ^{2m}(\omega x^{2n+1})$ / $x^{2l+1}\times \cosh ^{m}(\omega x^{2n})$ /XXXXXXXXXXXXXXXXXXXXXXXXXXXX $x^{2l+1}\times \tan ^{2m+1}(\omega x^{2n+1})$ / $x^{2l+1}\times \tan ^{m}(\omega x^{2n})$ / $x^{2l}\times \tan ^{2m+1}(\omega x^{2n+1})$ $x^{2l+1}\times \tanh ^{2m}(\omega x^{2n+1})$ / $x^{2l+1}\times \tanh ^{m}(\omega x^{2n})/x^{2l}\times \tanh ^{2m+1}(\omega x^{2n+1})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXX / $x^{2l+1}\times \exp ^{m}(\omega x^{2n})$ / XXXXXXXXXXXXXXXXXXXXXXXXXXXX
SinusAVEC Sin Cos Sinh Cosh Tan Tanh Exp	$\sin(\omega _{1}x)\times \sin ^{2m}(\omega _{2}x)$ $\sin(\omega _{1}x)\times \cos ^{m}(\omega _{2}x)$ $\sin(\omega _{1}x)\times \sinh ^{2m}(\omega _{2}x)$ $\sin(\omega _{1}x)\times \cosh ^{m}(\omega _{2}x)$ $\sin(\omega _{1}x)\times \tan ^{2m}(\omega _{2}x)$ $\sin(\omega _{1}x)\times \tanh ^{2m}(\omega _{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXX	$\sin(\omega _{1}x^{2l+1})\times \sin ^{m}(\omega x^{2})$ $\sin(\omega _{1}x^{2l+1})\times \cos ^{m}(\omega x^{2})$ $\sin(\omega _{1}x^{2l+1})\times \sinh ^{m}(\omega x^{2})$ $\sin(\omega _{1}x^{2l+1})\times \cosh ^{m}(\omega x^{2})$ $\sin(\omega _{1}x^{2l+1})\times \tan ^{m}(\omega x^{2})$ $\sin(\omega _{1}x^{2l+1})\times \tanh ^{m}(\omega x^{2})$ $\sin(\omega _{1}x^{2l+1})\times \exp ^{m}(\omega x^{2})$	$\sin(\omega _{1}x^{2l})\times \sin ^{2m+1}(\omega _{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX $\sin(\omega _{1}x^{2l})\times \sinh ^{2m+1}(\omega _{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX $\sin(\omega _{1}x^{2l})\times \tan ^{2m+1}(\omega _{2}x)$ $\sin(\omega _{1}x^{2l})\times \tanh ^{2m+1}(\omega _{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX	$\sin(\omega _{1}x^{2l+1})\times \sin ^{2m}(\omega _{2}x^{2n+1})$ / $\sin(\omega _{1}x^{2l+1})\times \sin ^{m}(\omega _{2}x^{2n})$ / $\sin(\omega _{1}x^{2l})\times \sin ^{2m+1}(\omega _{2}x^{2n+1})$ $\sin(\omega _{1}x^{2l+1})\times \cos ^{2m}(\omega _{2}x^{2n+1})$ / $\omega _{1}sin(x^{2l+1})\times \cos ^{m}(\omega _{2}x^{2n})$ /XXXXXXXXXXXXXXXXXXXXXXXXXXXX $\sin(\omega _{1}x^{2l+1})\times \sinh ^{2m}(\omega _{2}x^{2n+1})$ / $\sin(\omega _{1}x^{2l+1})\times \sinh ^{m}(\omega _{2}x^{2n})$ / $\sin(\omega _{1}x^{2l})\times \sinh ^{2m+1}(\omega _{2}x^{2n+1})$ $\sin(\omega _{1}x^{2l+1})\times \cosh ^{2m}(\omega _{2}x^{2n+1})$ / $\sin(\omega _{1}x^{2l+1})\times \cosh ^{m}(\omega _{2}x^{2n})$ / XXXXXXXXXXXXXXXXXXX $\sin(\omega _{1}x^{2l+1})\times \tan ^{2m}(\omega _{2}x^{2n+1})$ / $\sin(\omega _{1}x^{2l+1})\times \tan ^{m}(\omega _{2}x^{2n})$ / $\sin(\omega _{1}x^{2l})\times \tan ^{2m+1}(\omega _{2}x^{2n+1})$ $\sin(\omega _{1}x^{2l+1})\times \tanh ^{2m}(\omega _{2}x^{2n+1})$ / $\sin(\omega _{1}x^{2l+1})\times \tanh ^{m}(\omega _{2}x^{2n})/\sin(\omega _{1}x^{2l})\times \tanh ^{2m+1}(\omega _{2}x^{2n+1})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXX/ $\sin(\omega _{1}x^{2l+1})\times \exp ^{m}(\omega _{2}x^{2n})$ /XXXXXXXXXXXXXXXXXXXXXXXXXXXX
Cos AVEC Cos Sinh Cosh Tan Tanh Exp	XXXXXXXXXXXXXXXXXXXXXXXX $\cos(\omega _{1}x)\times \sinh ^{2m+1}(\omega _{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXX $\cos(\omega _{1}x)\times \tan ^{2m+1}(\omega _{2}x)$ $\cos(\omega _{1}x)\times \tanh ^{2m+1}(\omega _{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXX	XXXXXXXXXXXXXXXXXXXXXXXXXXXX $\cos(\omega _{1}x^{l})\times \sinh ^{2m+1}(\omega x^{2})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXX $\cos(\omega _{1}x^{l})\times \tan ^{2m+1}(\omega x^{2})$ $\cos(\omega _{1}x^{l})\times \tanh ^{2m+1}(\omega x^{2})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXX	XXXXXXXXXXXXXXXXXXXXXXXXXXX $\cos(\omega _{1}x^{l})\times \sinh ^{2m+1}(\omega _{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX $\cos(\omega _{1}x^{l})\times \tan ^{2m+1}(\omega _{2}x)$ $\cos(\omega _{1}x^{l})\times \tanh ^{2m+1}(\omega _{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX	XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX $\cos(\omega _{1}x^{2l+1})\times \sinh ^{2m+1}(\omega _{2}x^{2n+1})$ / $\cos(\omega _{1}x^{2l+1})\times \sinh ^{2m+1}(\omega _{2}x^{2n})$ / $\cos(\omega _{1}x^{2l})\times \sinh ^{2m+1}(\omega _{2}x^{2n+1})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX $\cos(\omega _{1}x^{2l+1})\times \tan ^{2m+1}(\omega _{2}x^{2n+1})$ / $\cos(\omega _{1}x^{2l+1})\times \tan ^{2m+1}(\omega _{2}x^{2n})$ / $\cos(\omega _{1}x^{2l})\times \tan ^{2m+1}(\omega _{2}x^{2n+1})$ $\cos(\omega _{1}x^{2l+1})\times \tanh ^{2m+1}(\omega _{2}x^{2n+1})$ / $\cos(\omega _{1}x^{2l+1})\times \tanh ^{2m+1}(\omega _{2}x^{2n})/\cos(\omega _{1}x^{2l})\times \tanh ^{2m+1}(\omega _{2}x^{2n+1})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
Cosh AVEC Sinh Cosh Tan Tanh Exp	$\cosh(\omega _{1}x)\times \sinh ^{2m+1}(\omega _{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXX $\cosh(\omega _{1}x)\times \tan ^{2m+1}(\omega _{2}x)$ $\cosh(\omega _{1}x)\times \tanh ^{2m+1}(\omega _{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXX	$\cosh(\omega _{1}x^{l})\times \sinh ^{2m+1}(\omega x^{2})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXX $\cosh(\omega _{1}x^{l})\times \tan ^{2m+1}(\omega x^{2})$ $\cosh(\omega _{1}x^{l})\times \tanh ^{2m+1}(\omega x^{2})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXX	$\cosh(\omega _{1}x^{l})\times \sinh ^{2m+1}(\omega _{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX $\cosh(\omega _{1}x^{l})\times \tan ^{2m+1}(\omega _{2}x)$ $\cosh(\omega _{1}x^{l})\times \tanh ^{2m+1}(\omega _{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX	$\cosh(\omega _{1}x^{2l+1})\times \sinh ^{2m+1}(\omega _{2}x^{2n+1})$ / $\cosh(\omega _{1}x^{2l+1})\times \sinh ^{2m+1}(\omega _{2}x^{2n})$ / $\cosh(\omega _{1}x^{2l})\times \sinh ^{2m+1}(\omega _{2}x^{2n+1})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX $\cosh(\omega _{1}x^{2l+1})\times \tan ^{2m+1}(\omega _{2}x^{2n+1})$ / $\cosh(\omega _{1}x^{2l+1})\times \tan ^{2m+1}(\omega _{2}x^{2n})$ / $\cosh(\omega _{1}x^{2l})\times \tan ^{2m+1}(\omega _{2}x^{2n+1})$ $\cosh(\omega _{1}x^{2l+1})\times \tanh ^{2m+1}(\omega _{2}x^{2n+1})$ / $\cosh(\omega _{1}x^{2l+1})\times \tanh ^{2m+1}(\omega _{2}x^{2n})/\cosh(\omega _{1}x^{2l})\times \tanh ^{2m+1}(\omega _{2}x^{2n+1})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
Tan AVEC Tan Tanh Exp	$\tan(\omega _{1}x)\times \tan ^{2m}(\omega _{2}x)$ $\tan(\omega _{1}x)\times \tanh ^{2m}(\omega _{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXX	$\tan(\omega _{1}x^{2l+1})\times \tan ^{2m+1}(\omega x^{2})$ $\tan(\omega _{1}x^{2l+1})\times \tanh ^{2m+1}(\omega x^{2})$ $\tan(\omega _{1}x^{2l+1})\times \exp ^{m}(\omega x^{2})$	$\tan(\omega _{1}x^{2l})\times \tan ^{2m+1}(\omega _{2}x)$ $\tan(\omega _{1}x^{2l})\times \tanh ^{2m+1}(\omega _{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX	$\tan(\omega _{1}x^{2l+1})\times \tan ^{2m+1}(\omega _{2}x^{2n+1})$ / $\tan(\omega _{1}x^{2l+1})\times \tan ^{2m+1}(\omega _{2}x^{2n})$ / $\tan(\omega _{1}x^{2l})\times \tan ^{2m+1}(\omega _{2}x^{2n+1})$ $\tan(\omega _{1}x^{2l+1})\times \tanh ^{2m}(\omega _{2}x^{2n+1})$ / $\tan(\omega _{1}x^{2l+1})\times \tanh ^{2m+1}(\omega _{2}x^{2n})/\tan(\omega _{1}x^{2l})\times \tanh ^{2m+1}(\omega _{2}x^{2n+1})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
Tanh AVEC Tanh Exp	$\tanh(\omega _{1}x)\times \tanh ^{2m}(\omega _{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXX	$\tanh(\omega _{1}x^{2l+1})\times \tanh ^{2m+1}(\omega x^{2})$ $\tanh(\omega _{1}x^{2l+1})\times \exp ^{m}(\omega x^{2})$	$\tanh(\omega _{1}x^{2l})\times \tanh ^{2m+1}(\omega _{2}x)$ XXXXXXXXXXXXXXXXXXXXXXXXXXX	$\tanh(\omega _{1}x^{2l+1})\times \tanh ^{2m}(\omega _{2}x^{2n+1})$ / $\tanh(\omega _{1}x^{2l+1})\times \tanh ^{2m+1}(\omega _{2}x^{2n})/\tanh(\omega _{1}x^{2l})\times \tanh ^{2m+1}(\omega _{2}x^{2n+1})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX $\tan(\omega _{1}x^{2l+1})\times \exp ^{m}(\omega x^{2})$ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
Construite Approchée

Dans les approches A et C modifier

Techniques de régressions au plus près

Définition de la régression au plus près

Fonctions régressives Fi communes composées